Related papers: On Matrix Product Factorization of graphs

Coloring the arcs of biregular graphs was introduced with possible applications to industrial chemistry, molecular biology, cellular neuroscience, etc. Here, we deal with arc coloring in some non-bipartite graphs. In fact, for…

We analyze effective approximation of unitary matrices. In our formulation, a unitary matrix is represented as a product of rotations in two-dimensional subspaces, so-called Givens rotations. Instead of the quadratic dimension dependence…

In this paper, we introduce a new concept namely degree polynomial for vertices of a simple graph. This notion leads to a concept namely degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the…

Let $X$ be an infinite graph of bounded degree; e.g., the Cayley graph of a free product of finite groups. If $G$ is a finite graph covered by $X$, it is said to be $X$-Ramanujan if its second-largest eigenvalue $\lambda_2(G)$ is at most…

We study the problem of transforming bipartite graphs into bicluster graphs. Abu-Khzam, Isenmann, and Merchad [IWOCA '25] introduced two variants of this problem. In both problems, the goal is to transform a bipartite graph into a bicluster…

This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…

Recently, Bapat and Kurata [\textit{Linear Algebra Appl.}, 562(2019), 135-153] defined the Cartesian product of two square matrices $A$ and $B$ as $A\oslash B=A\otimes \J+\J\otimes B$, where $\J$ is the all one matrix of appropriate order…

Graph product is a fundamental tool with rich applications in both graph theory and theoretical computer science. It is usually studied in the form $f(G*H)$ where $G$ and $H$ are graphs, * is a graph product and $f$ is a graph property. For…

We consider the algebra M_k(C) of k-by-k matrices over the complex numbers and view it as a crossed product with a group G of order k by embedding G in the symmetric group S_k via the regular representation and embedding S_k in M_k(C) in…

A factor of a graph is a spanning subgraph satisfying some given conditions. An earlier survey of factors can be traced back to the Akiyama and Kano [J. Graph Theory, 1985, 9: 1-42] in which they described the characterization of factors in…

It was recently proved that every planar graph is a subgraph of the strong product of a path and a graph with bounded treewidth. This paper surveys generalisations of this result for graphs on surfaces, minor-closed classes, various…

Data often comes in the form of an array or matrix. Matrix factorization techniques attempt to recover missing or corrupted entries by assuming that the matrix can be written as the product of two low-rank matrices. In other words, matrix…

We enumerate factorisations of the complete bipartite graph into spanning semiregular graphs in several cases, including when the degrees of all the factors except one or two are small. The resulting asymptotic behaviour is seen to…

A spanning subgraph of a graph G is called a [0,2]-factor of G, if for . is a union of some disjoint cycles, paths and isolate vertices, that span the graph G. It is easy to get a [0,2]-factor of G and there would be many of [0,2]-factors…

Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…

While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…

Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…

A graph property (i.e., a set of graphs) is induced-hereditary or additive if it is closed under taking induced-subgraphs or disjoint unions. If $\cP$ and $\cQ$ are properties, the product $\cP \circ \cQ$ consists of all graphs $G$ for…

A graph $G$ is said to be an $(s, k)$-polar graph if its vertex set admits a partition $(A, B)$ such that $A$ and $B$ induce, respectively, a complete $s$-partite graph and the disjoint union of at most $k$ complete graphs. Polar graphs and…

Boxicity of a graph $G(V,E)$ is the minimum integer $k$ such that $G$ can be represented as the intersection graph of $k$-dimensional axis parallel rectangles in $\mathbf{R}^k$. Equivalently, it is the minimum number of interval graphs on…